Simplify. Write your answers in the form of a+bi, where a and b are real numbers.
-$\frac { i } { 5 + i }$
A) $\frac { 5 } { 26 } \mathrm { i }$
B) $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$
C) $\frac { 1 } { 26 } - \frac { 5 } { 26 } \mathrm { i }$
D) $\frac { 1 } { 26 }$

Question

Quizplus · Accepted Answer

To simplify $\frac { i } { 5 + i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $5 - i$. This results in $\frac { i(5 - i) } { (5 + i)(5 - i) }$ = $\frac { 5i - i^2 } { 25 - i^2 }$ = $\frac { 5i + 1 } { 26 }$ = $\frac { 1 } { 26 } + \frac { 5 } { 26 } \mathrm { i }$.

Simplify Write Your Answers in the Form of A+bi, Where i5+i\frac { i } { 5 + i }5+ii​

Simplify Write Your Answers in the Form of A+bi, Where $\frac { i } { 5 + i }$